Field of Applicable Technology
The present invention relates to a noise shaping requantization circuit for use in converting a digital signal to an analog signal by employing a low resolution digital/analog converter. Such a requantization circuit functions by requantizing the digital signal to convert it to a digital signal having a lower degree of resolution, with the requantization being executed such that the frequency distribution of the resampling noise that is generated in the requantization process is shaped such as to shift the noise components to a high frequency range, thereby effectively increasing the signal-to-noise ratio of the output digital signal.
Noise shaping quantization methods for use in achieving a high accuracy of D/A conversion operation are now well known, whereby an input digital signal (originally generated by sampling of an analog signal at an original sampling frequency which is higher than the minimum, i.e. Nyquist sampling frequency) is resampled and requantized using a resampling frequency that is substantially higher than the original sampling frequency (i.e. oversampling is executed) and using a requantization step size that is substantially larger than the original quantization step size of the input digital signal (i.e. a lower degree of resolution is used than that used to derive the original digital signal) In general, negative feedback is applied, to produce a differential characteristic for the amplitude/frequency spectrum of the quantization error noise that is generated as a result of that sampling operation. As a result, in effect the quantization noise contained in the output digital signal is shifted outside the desired signal frequency range, and the level of quantization noise within the desired signal frequency range is reduced. The resampled output digital signal is then converted to analog form by a D/A conversion section. Due to the large step size, i.e. low resolution of the requantization, this D/A conversion section can have a very simple configuration and provide very high conversion accuracy.
A D/A converter based on such a noise shaping requantization circuit is used in two basic types of application, i.e. for D/A conversion or for A/D conversion. In the case of D/A conversion, an original input digital signal is resampled as described above, and the resultant requantized output digital signal is supplied to a D/A conversion section, to be converted to analog form. In the case of A/D conversion, an original analog signal is sampled at an original sampling frequency (i.e. at least higher than the Nyquist frequency for the input signal frequency range), and the resultant output digital signal is then inputted to an internal noise shaping requantization circuit, to obtain a requantized digital signal which is then transferred through an internal D/A conversion section to obtain an analog signal which is fed back to the input such as to form a negative feedback loop. The accuracy of the output digital signal is thereby increased.
In the case of an A/D converter which incorporates such an internal digital/analog converter for negative feedback purposes, the oversampling technique enables the internal configuration to be made very simple, since the internal D/A conversion can have a very low degree of resolution (e.g. with a total of only two or three quantization steps). This serves to eliminate any problems of linearity errors in the internal D/A conversion, and makes it unnecessary to perform adjustment or trimming of the circuit. In addition, such a configuration can readily be adapted to implementation in integrated circuit form.
Similar advantages are obtained when such a noise shaping quantization method is applied to a digital/analog converter for producing an output analog signal from an original digital signal. Here again a quantized output digital signal having a lower degree of resolution than the input digital signal (i.e. larger quantization step size) can be produced, which can then be subjected to digital-to-analog conversion by a low-resolution digital/analog converter, to obtain the desired output analog signal. Hence, the overall digital/analog converter can be easily realized in integrated circuit form.
The advantage is also obtained that a simple digital/analog converter section having low resolution but a very high degree of linearity, such as a PWM (pulse width modulation) type of digital/analog converter circuit can be used to convert the requantized digital signal to analog form with a very high degree of accuracy.
For these reasons, various types cf noise shaping quantization methods have been developed in recent years, and are now known in the art.
FIG. 1A is a block diagram of a prior art noise shaping requantization circuit (referred to in the following simply as a requantization circuit), which utilizes a method of requantization that is a development of the delta-sigma method. The circuit of FIG. 1A provides a fourth order noise shaping characteristic. In FIG. 1A, numeral 5 denotes an input terminal of an input digital signal X(z), 7 denotes a requantizer for converting the input digital signal to an output signal Y'(z) having a lower degree of resolution than the input digital signal, 6 denotes an output terminal for transferring an output signal produced from the requantizer 7, 8 to 11 denote subtractors, 12 to 15 denote adders. 16 to 20 denote delay elements each of which provides a unit delay that is equal to one resampling period.
The requantization circuit of FIG. 1A provides a fourth order noise shaping characteristic as stated above. However if subtractor 11, adder 15 and delay element 20 in FIG. 1A are removed, and the output signal from the adder 14 applied directly to &he requantizer 7, then the circuit will provide a third order noise shaping characteristic. Such a prior art requantization circuit for providing a third order noise shaping characteristic is shown in FIG. 1B, and will be referred to in the following as the prior art example No. 1. The requantization circuit of FIG. 1A, which provides a fourth order noise shaping characteristic, will be referred to in the following as the prior art example No. 2.
In the following, all signals will be expressed in z-plane form, based on the resampling period, which corresponds to a delay operator that is designated in the following as z.sup.-1. Such a manner cf expressing signals consisting of successive samples is now widely utilized. With the requantization circuit of FIGS. 1A, 1B designating the requantization error of the low resolution converted output from the requantizer 7 as N(z), designating the input signal to the requantizer 7 as A'(z), and designating the output signal from the requantization circuit as Y'(z), then the following is true:
ti Y'(z)=A'(z)+N(z) . . . (1)
In addition, the relationship between the input signal A'(z) of the requantizer 7 and the output signal Y'(z) of the requantization circuit is given by the following equation (2): ##EQU1##
In the above, K is a natural number. With the prior art example No. 1, K=3, while with the prior art example No. 2, K=4.
The input signal A'(z) of the requantizer 7 and the output signal Y'(z) from the requantization circuit, given by the equations (1) and (2) above, can be expressed by the following equations (3) and (4) respectively: EQU A'(z)=X(z)+{(1-z.sup.-1).sup.K -1}.multidot.N(z) . . . (3) EQU Y'(z)=X(z)+(1-z.sup.-1).sup.K .multidot.N(z) . . . (4)
As is known in the art, the term ((1-z.sup.-1)).sup.K provides a differential characteristic, whereby gain varies in proportion to frequency such that the amplitude of the quantization error (quantization noise) components of the output signal expressed by equation (4) will be reduced in accordance with lowering of frequency. That is to say, the desired noise shaping characteristic is exhibited. The factor K in the above equations expressed the order of the noise shaping circuit.
The requantization circuit of the prior art example No. 1 exhibits a third order noise shaping characteristic, while the requantization circuit of the prior art example No. 2 exhibits a fourth order noise shaping characteristic.
With a requantization circuit, as will be clear from the above equation (4), the greater the value of K (i.e. the higher the order of the circuit), the greater will become the improvement that is provided in the signal-to-noise ratio within the signal frequency range.
On the other hand, as can be seen from equation (3) above, the higher the value of K, the greater will become the level of the input signal A'(z) of the requantizer 7. That is to say, assuming that the quantization step size of the requantizer 7 is 2P (where P is an arbitrary natural number), and also assuming that the requantizer 7 is not driven into saturation (i.e. that the requantization error N(z) will always be within the range .+-.P), then the range of the requantization error N(z) is expressed as follows: EQU -P.ltoreq.N(z).ltoreq.P . . . (5)
Moreover, from equation (3) above, the following can be expressed: EQU -(2.sup.K -1).multidot.P.ltoreq.{A'(z)-X(z)}.ltoreq.{(2.sup.K -1).multidot.P}. . . (6)
The above relationship (6) signifies that the limits of the input signal A'(z) of the requantizer 7 are widened with respect to the limits of the input signal X(z), by the amount .+-.(2.sup.K -1).multidot.P, and hence, the higher is the order K, the greater will become the level of the input signal A'(z) of the requantizer 7, and hence, the greater will become the necessary number of output steps of the requantizer 7 (i.e. the higher will become the necessary degree of resolution). For example the limits of the input signal A'(z) of the requantizer 7 are wider than the limits of the input digital signal by the amount .+-.7P, in the case of the prior art example No. 1, while the limits of the input signal A'(z) of the requantizer 7 are wider than the limits of the input digital signal by the amount .+-.15P, in the case of the prior art example No. 2. Hence, the required degree of resolution of the requantizer 7 must be accordingly increased.
The above points signify that the resolution of the digital/analog converter which receives the output signal of the requantization circuit must be increased in accordance with an increase of the order K of the requantization circuit. Hence, this counteracts the basic objective of using such a requantization circuit, which is to enable a reduction of the required degree of resolution of the digital/analog converter that is connected to receive the output digital signal from the requantization circuit.
For example if a PWM (pulse width modulation) type of digital/analog converter is used as the digital/analog converter that is supplied with the output signal from the requantization circuit, then if the degree of resolution that is necessary for that digital/analog converter is increased, the clock frequency of the digital/analog converter must be accordingly increased. This will lead to various practical problems, and so is basically, undesirable. For example, as a result of the need to generate a higher frequency of clock signal, it is difficult to use an inexpensive type of oscillator vibrator element for generating the clock signal, and it is also necessary to use circuit elements which can function at higher frequencies, in order to prevent any reduction of conversion accuracy. Thus, various problems will arise with regard to practical realization of such prior art types of noise shaping requantization circuit.